松本 洋介

We present a new numerical scheme for solving the advection equation and its application to the Vlasov simulation. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, and advances them on the basis of their governing equations. We have developed one- and two-dimensional schemes and show that they provide quite accurate solutions compared to other existing schemes with the same memory usage. The two-dimensional scheme can solve the solid body rotation problem of a gaussian profile with little numerical diffusion. This is a very important property for Vlasov simulations of magnetized plasma. The application of the scheme to the electromagnetic Vlasov simulation of collisionless shock waves is presented as a benchmark test.

Recently, numerical techniques for Vlasov simulations are advanced, and they are applied to cross-scale coupling in space plasmas. This paper presents recent attempts to understand particle kinetics in macroscopic phenomena such as magnetic reconnection and the Kelvin-Helmholtz instability via Vlasov codes, suggesting that the Vlasov simulation would be a powerful approach for studies of cross-scale coupling in space plasmas.